Question

Occasionally, an airline will lose a bag. A small airline has found it loses an average of 5 bags each day. Find the probability that on a given day,

a) The airline loses exactly 14 bags.
b) The airline loses fewer than 14 bags.
c) The airline loses more than 12 bags.

Answer 1

To find the probability that the airline loses a specific number of bags, you can use the Poisson distribution formula. The probabilities of losing fewer or more bags can be calculated by summing up the probabilities for each value.

Step-by-step explanation:

To find the probability that the airline loses exactly 14 bags, we can use the Poisson distribution formula. The average number of bags lost per day is 5, so the parameter lambda for the Poisson distribution is also 5. Substituting this value into the formula, we get:

P(X = 14) = (e^-5 * 5^14) / 14! = 0.021.

To find the probability that the airline loses fewer than 14 bags, we can sum up the probabilities of losing 0, 1, 2, ..., 13 bags. P(X < 14) = P(X = 0) + P(X = 1) + ... + P(X = 13). The probability can be calculated using the Poisson distribution formula for each value and then adding them up.

To find the probability that the airline loses more than 12 bags, we can sum up the probabilities of losing 13, 14, 15, ... bags. P(X > 12) = P(X = 13) + P(X = 14) + ... The probabilities can be calculated using the Poisson distribution formula for each value and then adding them up.